Corpus ID: 218684701

The Rectangular Peg Problem

@article{Greene2020TheRP,
title={The Rectangular Peg Problem},
author={Joshua Evan Greene and Andrew Lobb},
journal={arXiv: Geometric Topology},
year={2020}
}
• Published 2020
• Mathematics
• arXiv: Geometric Topology
• For every smooth Jordan curve $\gamma$ and rectangle $R$ in the Euclidean plane, we show that there exists a rectangle similar to $R$ whose vertices lie on $\gamma$. The proof relies on Shevchishin's theorem that the Klein bottle does not admit a smooth Lagrangian embedding in $\mathbb{C}^2$.

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